^=read as to the power *=read as square root As per question 6x^3+13x^2+2x-5=0 6x^3+13x^2+2x=5 6x^3+12x^2+x^2+2x=5 6x^2(x+2)+x(x+2)=5 (X+2)(6x^2+x)=5 (X+2)(6x^2+x)=(1×5) or (5×1) Let's take (1×5) So, (X+2)(6x^2+x)=1×5 So, case 1 X+2=1 X=1-2=(-1) Again 6x^2+x=5 6x^2+x-5=0 6x^2+6x-5x-5=0 6x(x+1)-5(x+1)=0 (6x-5)(x+1)=0 6x-5=0 or x+1=0 6x=5 or x=(-1) X=(5/6), or x=(-1) Case 2......(5×1) So, X+2=5 X=5-2=3 Again 6x^2+x=1 6x^2+x-1=0 Here a=6, b=1,c=-1 D=b^2-(4ac) =(1^2)-(4×6×-1) =1+24=25 *D=*(25)=5 X={(-1)±5}/(2×6) ={(-1)±5}/12 =(-1-5)/12, or (-1+5)/12 =(-6)/12, or 4/12 =-(1/2), or (1/3)
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^=read as to the power
*=read as square root
As per question
6x^3+13x^2+2x-5=0
6x^3+13x^2+2x=5
6x^3+12x^2+x^2+2x=5
6x^2(x+2)+x(x+2)=5
(X+2)(6x^2+x)=5
(X+2)(6x^2+x)=(1×5) or (5×1)
Let's take (1×5)
So,
(X+2)(6x^2+x)=1×5
So, case 1
X+2=1
X=1-2=(-1)
Again
6x^2+x=5
6x^2+x-5=0
6x^2+6x-5x-5=0
6x(x+1)-5(x+1)=0
(6x-5)(x+1)=0
6x-5=0 or x+1=0
6x=5 or x=(-1)
X=(5/6), or x=(-1)
Case 2......(5×1)
So,
X+2=5
X=5-2=3
Again
6x^2+x=1
6x^2+x-1=0
Here a=6, b=1,c=-1
D=b^2-(4ac)
=(1^2)-(4×6×-1)
=1+24=25
*D=*(25)=5
X={(-1)±5}/(2×6)
={(-1)±5}/12
=(-1-5)/12, or (-1+5)/12
=(-6)/12, or 4/12
=-(1/2), or (1/3)
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